Blender Game Character Jumping Issues
The blender game engine has a special function for jumping: first, make sure the Physics Type for your character is set to "Character". Then, in the Motion actuator, set Motion Type to "Character Motion", leave all the numbers at zero and set the "Jump" button. As the tooltip says, the settings for that are in the Properties panel, Physics tab (right underneath the Physics Type).

If you can't use the Character type for whatever reason, another way to make it work (the old way) is to add a collision sensor that references the ground, then "and" that with your keyboard sensor.

FYI: this seems to be a duplicate of How to create a realistic jump in bge, but since I don't have enough rep to flag it as such, I answered instead.